No.  There is only a single hospitals list that is used for all programs in the database.

You must have the "Display Any Chart Records Buttons" and the "Display Chart Records Hospital Button" data entry/access permissions in order to access the Hospital module in which the Hospital feature is located and from which additions/changes to the hospitals list can be made.  (One exception to this rule is made for users who select the "Other" option while entering a hospitalization record; such users can add to the hospitals list, regardless of their permission assignment.)